Water Hammer and Column Separation Induced by Simultaneous and Delayed Closure of Two Valves

Water hammer and column separation induced by simultaneous and sequential (delayed) closure of two valves may occur in industrial pipeline systems. This paper deals with such cases both experimentally and numerically. Water hammer equations are solved by the method of characteristics. Transient cavitating pipe flow is simulated by a discrete gas cavity model (DGCM) that considers unsteady skin friction. Discrete gas cavities and Zielke's convolution-based unsteady skin friction term are explicitly incorporated in the staggered grid algorithm of the method of characteristics. Experiments have been performed in a laboratory pipeline apparatus. The apparatus consists of an upstream end tank, a horizontal steel pipeline (total length 55.37 m, inner diameter 18 mm), four valve units positioned along the pipeline including the end points, and a downstream end tank. A transient event is induced either by simultaneous or sequential closure of two end valves. Numerical results are compared and verified with results of measurements. In addition, a theoretical analysis of pressure wave fronts travelling along the pipeline is also presented to clearly show profound effects of wave interactions.